Abstract
Results on singularly perturbed control obtained since 1982 are reviewed.
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Azizov, T.Ya., Kiriakidi, V.K., and Kurina, G.A., Reducibility of a Nonnegative Hamiltonian Operator Function to Block Diagonal Matrix Form: An Indefinite Approach, Funk. Anal. Pril., 2001, vol. 35, no. 3, pp. 73–75.
Akulenko, L.D., Asimptoticheskie metody optimal’nogo upravleniya (Asymptotic Methods of Optimal Control), Moscow: Nauka, 1987.
Arutyunov, A.V., Usloviya ekstremuma. Anormal’nye i vyrozhdennye zadachi (Extremum Conditions. Abnormal and Degenerate Problems), Moscow: Faktorial, 1997.
Belokopytov, S.V. and Dmitriev, M.G., A Direct Solution Method for Optimal Control Problems with Fast and Slow Motions, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1985, no. 3, pp. 147–152.
Belokopytov, S.V. and Dmitriev, M.G., Solution of Classical Optimal Control Problems with a Boundary Layer, Avtom. Telemekh., 1989, no. 7, pp. 71–82.
Belokopytov, S.V., Dmitriev, M.G., and Overzov, Kh.A., Design of Suboptimal Controls for Linear Quadratic Problems Close to Degenerate Problems, in Informatika i sistemnyi analiz (Information and System Analysis), Ashkhabad, 1990, pp. 4–19.
Binning, H.S. and Goodall, D.P., Output Control for Uncertain Singularly Perturbed Nonlinear Systems, Avtom. Telemekh., 1997, no. 7, pp. 81–97.
Bobodzhanov, A.A., Limit Transition in Singularly Perturbed Integral Systems and Optimal Control Problems, Dokl. Ross. Akad. Nauk, 2001, vol. 379, no. 6, pp. 727–729.
Bobodzhanov, A.A., Asymptotic Solutions for Singularly Perturbed Control Systems with Rapidly Varying Damping, Mat. Modelirovanie, 2001, vol. 13, no. 11, pp. 116–126.
Borzov, V.I. and Igonina, T.R., A Maximal Flight Range Problem, Izv. Akad. Nauk SSSR, Mekh. Tverdogo Tela, 1982, no. 2, pp. 20–24.
Brusin, V.A., A Class of Singularly Perturbed Adaptive Systems. I, Avtom. Telemekh., 1995, no. 4, pp. 119–129.
Brusin, V.A., A Class of Singularly Perturbed Adaptive Systems. II, Avtom. Telemekh., 1995, no. 5, pp. 103–113.
Buruzov, V.F., Vasil’eva, A.B., and Nefedov, N.N., Asymptotic Theory of Contrast Structures (A Review), Avtom. Telemekh., 1997, no. 7, pp. 4–32.
Vasil’eva, A.B. and Butuzov, V.F., Asimptoticheskie metody v teorii singulyarnykh vozmushchenii (Asymptotic Methods in Singular Perturbation Theory), Moscow: Vysshaya Shkola, 1990.
Vasil’eva, A.B. and Dmitriev, M.G., Singular Perturbations in Optimal Control Problems, Itogi Nauki i Tekhniki, Mat. Analiz, 1982, vol. 20, pp. 3–77.
Vasil’eva, A.B. and Dmitriev, M.G., Singular Perturbations in Nonlinear Optimal Control Problems, in Aktyal. problemy mat. fiz. i vychisl. mat. (Topical Problems in Mathematical Physics and Computational Mathematics), Moscow: Nauka, 1984, pp. 40–49.
Vel’ov, V.M. and Donchev, A.L., Continuity of Trajectories of Linear Control Systems with Respect to Singular Perturbations, Dokl. Akad. Nauk SSSR, 1987, vol. 293, no. 2, pp. 274–278.
Gabasov, R., Kirillova, F.M., and Asmykovich, I.K., Deskriptornye sistemy upravleniya: bibliograf. ukazatel’ (Descriptor Control Systems: A Bibliography Index), Minsk: Inst. Mat., 1988.
Gaipov, M.A., An Asymptotic Solution to a Nonlinear Discrete Optimal Control Problem with a Small Step without Control Constraints (Formalism). I, Izv. Akad. Nauk TSSR, FTKh i GN, 1990, no. 1, pp. 9–16.
Gaipov, M.A., An Asymptotic Solution to a Discrete Singularly Perturbed Optimal Control Problem under Phase Constraints, in Informatika i sistemnyi analiz (Information and System Analysis), Ashkhabad, 1990, pp. 43–53.
Gaipov, M.A. and Dmitriev, M.G., Controllability of a Discrete Time-varying Linear System with a Small Step, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1998, no. 2, pp. 44–46.
Gaitsgory, V.G., Upravlenie sistemami s bystrymi i medlennymi dvizheniyami (Control for Systems with Slow and Fast Motions), Moscow: Nauka, 1991.
Gichev, T.R., Singular Perturbations in a Linear Differential Pursuit Game, God. VUZ. Prilozh. Mat., 1981 (1982), vol. 17, no. 3, pp. 9–20.
Gichev, T.R., Controllability of a Linear Singularly Perturbed Delay System, Tr. 3 Konf., Russe, part 1, 1987, pp. 83–86.
Gichev, T.R., Controllability of a Singularly Perturbed System in Certain Critical Cases, God. VUZ. Prilozh. Mat., 1986 (1987), vol. 22, no. 1, pp. 31–42.
Glizer, V.Ya., An Asymptotic Solution to a Singularly Perturbed Cauchy Problem in Linear Optimal Filtering Theory, Izv. VUZov. Mat., 1984, no. 12, pp. 55–58.
Glizer, V.Ya., A Difference Optimal Control Problem with a Small Step, Diff. Uravn., 1985, vol. 21, no. 8, pp. 1440–1442.
Glizer, V.Ya., An Asymptotic Solution of the Cauchy Problem for a Matrix Riccati Differential Equation with Two Small Parameters, Diff. Uravn., 1987, vol. 23, no. 3, pp. 517, 518.
Glizer, V.Ya., An Asymptotic Solution to a Difference Optimal Control Problem with a Small Step and Moving Trajectory Right End, Diff. Uravn., 1988, vol. 24, no. 8, pp. 1457–1459.
Glizer, V.Ya., Singular Perturbations in a Stochastic Linear Quadratic Optimal Control Problem, Diff. Uravn., 1990, vol. 26, no. 5, pp. 753–759.
Gornov, A.Yu., Dmitriev, M.G., and Tyatyushkin, A.I., Opyt resheniya zadach optimal’nogo upravleniya s pogranichnym sloem (Solution of Optimal Control Problems with a Boundary Layer), Available from VINITI, 1985, Krasnoyarsk, no. 28441-1385.
Danilin, A.R., Asymptotic Bounded Controls for a Singularly Perturbed Elliptical Problem in a Hollow Domain, Mat. Sb., 1998, vol. 189, no. 11, pp. 27–60.
Danilin, A.R., Approximation of a Singularly Perturbed Elliptical Optimal Control Problem, Mat. Sb., 2000, vol. 191, no. 10, pp. 3–12.
Danilin, A.R. and Il’in, A.M., Asymptotic Behavior of the Solution of a Time-Optimal Problem for a Linear System under Perturbed Initial Conditions, Dokl. Ross. Akad. Nauk, 1996, vol. 350, no. 2, pp. 155–157.
Danilin, A.R. and Il’in, A.M., The Structure of the Solution of a Perturbed Time-Optimal Problem, Fund. Prikl. Mat., 1998, vol. 4, no. 3, pp. 905–926.
Dmitriev, M.G., The Continuity of the Solution of the Meyer Singular Perturbation Problem, Zh. Vychisl. Mat. Mat. Fiz., 1972, vol. 12, no. 3, pp. 788–791.
Dmitriev, M.G., An Iterative Solution to an Optimal Control Problem with Fast and Slow Motions, Dokl. Akad. Nauk SSSR, 1983, vol. 272, no. 2, pp. 281–284.
Dmitriev, M.G., Boundary Layer in Optimal Control Problems, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1983, no. 4, pp. 63–69.
Dmitriev, M.G., Singular Perturbations in Optimal Control Problems, Doctoral (Phys.-Math.) Dissertation, Moscow: Mosk. Gos. Univ., 1984.
Dmitriev, M.G., Belokopytov, S.V., and Gaipov, M.A., An Asymptotic Solution to a Nonlinear Discrete Optimal Control Problem with a Small Step without Control Constraints (Proof). II, Izv. Akad. Nauk TSSR, FTKh GN, 1990, no. 2, pp. 10–18.
Dmitriev, M.G. and Kang Ni Ming, Contrast Structures in a Simple Vector Variational Problem and Their Asymptotes, Avtom. Telemekh., 1998, no. 5, pp. 41–52.
Dmitriev, M.G. and Kang Ni Ming, Asymptotes of Contrast Extremals in a Simple Vector Variation Problem, Fund. Prikl. Mat., 1998, vol. 4, no. 4, pp. 1165–1178.
Dmitriev, M.G. and Kang Ni Ming, An Asymptotic Solution with Internal Transition in a Simple Variational Problem, in Programmnye sistemy. Teoreticheskie osnovy i prilozheniya (Programmed Systems: Theoretical Principles and Applications), Moscow: Inst. Prog. Sistem, 1999, pp. 56–65.
Dmitriev, M.G. and Klishevich, A.M., An Iterative Solution Method for a Problem on Output Controller with Slow and Fast Motions, Preprint of Computing Center, Siberian Branch, USSR Acad. Sci., Krasnoyarsk, 1983, no. 2.
Dmitriev, M.G. and Klishevich, A.M., Iterative Solution Methods for Singularly Perturbed Conditionally Stable Boundary-Value Problems, Zh. Vychisl. Mat. Mat. Fiz., 1987, vol. 27, no. 12, pp. 1812–1823.
Dmitriev, M.G. and Konyaev, Yu.A., The Birkhoff Asymptote of Certain Singularly Perturbed Optimal Control Problems, Mat. Modelirovanie, 2002, vol. 14, no. 3, pp. 27–29.
Dmitriev, M.G. and Kurina, G.A., A Direct Scheme of Asymptotic Solution for Classical Optimal Control Problems, in Programmnye sistemy. Teoreticheskie osnovy i prilozheniya (Programmed Systems: Theoretical Principles and Applications), Ailamazyan, A.K., Ed., Moscow: Nauka, 1999, pp. 44–55.
Dmitriev, M.G., Kurina, G.A., and Ovezov, Kh.A., A Direct Solution Scheme for Singularly Perturbed Linear Quadratic Optimal Control Problems, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1996, no. 4, pp. 62–68.
Dmitriev, M.G. and Soltanov, S.T., An Asymptote of Outer Ellipsoidal Estimates for Reachable Sets of Linear Singularly Perturbed Control Systems, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1996, no. 3, pp. 51–54.
Dmitriev, M.G. and Yan’shin, V.N., A Nonlinear Periodic Optimal Control Problem for a System with a Small Parameter at Derivatives, Ukr. Mat. Zh., 1987, vol. 39, no. 3, pp. 289–295.
Donchev, A., Sistemy optimal’nogo upravleniya. Vozmushcheniya, priblizheniya i analiz chuvstvitel’nosti (Optimal Control Systems: Perturbation, Approximation, and Sensitivity Analysis), Moscow: Mir, 1987.
Egorov, A.I. and Mikhailova, T.F., Singular Perturbations in Optimal Heat Stabilization Problems, Dokl. Akad. Nauk SSSR, A, 1986, no. 3, pp. 74–77.
Egorov, A.I. and Mikhailova, T.F., Angular Boundary Functions in a Singularly Perturbed Heat Control Problem, in Optimizatsionnyi sintez v sistemakh s raspredelennymi parametrami (An Optimization Design for Distributed-Parameter Systems), Frunze: ILIM, 1989, pp. 3–12.
Zharikova, E.N. and Sobolev, V.A., Optimal Periodic Control Systems with Singular Perturbations, Avtom. Telemekh., 1997, no. 7, pp. 151–168.
Zelikin, M.I., Odnorodnye prostranstva i uravnenie Riccati v variatsionnom ischislenii (Homogeneous Spaces and Riccati Equations in Variational Calculus), Moscow: Faktorial, 1998.
Il’in, A.M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach (Matching of Asymptotic Expansions of Solutions of Boundary-Value Problems), Moscow: Nauka, 1989.
Il’in, A.M., Danilin, A.R., and Zakharov, S.V., Application of Asymptotic Expansion Splicing in Boundary-Value Problems, in Sovremennaya matematika i ee prilozheniya. T. 5. Asimptoticheskie metody funktsional’nogo analiza (Modern Mathematics and Its Applications. Asymptotic Methods of Functional Analysis), Institute of Cybernetics, Georgian Academy of Sciences, 2003, pp. 33–78.
Ishmukhametov, A.Z., Controllability of Hyperbolic Systems under Singular Perturbations, Diff. Uravn., 2000, vol. 36, no. 2, pp. 241–250.
Ishmukhametov, A.Z., Control for Singularly Perturbed Hyperbolic Systems: Conditions and Estimates for the Convergence of Solutions, Diff. Uravn., 2000, vol. 36, no. 6, pp. 774–783.
Ishmukhametov, A.Z., Voprosy ustoichivosti i approksimatsii zadach optimal’nogo upravleniya sistemami s raspredelennymi parametrami (Stability and Approximation of Optimal Control for Distributed-Parameter Systems), Moscow: Vychisl. Tsentr Akad. Nauk SSSR, 2001.
Kalinin, A.I., An Algorithm for Asymptotically Solving a Singularly Perturbed Time-Optimal Linear Problem, Prikl. Mat. Mekh., 1989, vol. 53, no. 6, pp. 880–889.
Kalinin, A.I., An Asymptotic Solution Method for Singularly Perturbed Linear Terminal Control Problems, Zh. Vychisl. Mat. Mat. Fiz., 1990, vol. 30, no. 3, pp. 366–378.
Kalinin, A.I., An Asymptotic Solution to a Linear Optimal Control Problem with a Long Process Duration, Dokl. Belarus. Nat. Akad. Nauk, 1991, vol. 35, no. 6, pp. 488–491.
Kalinin, A.I., An Algorithm for Asymptotically Solving Singularly Perturbed Nonlinear Time-Optimal Problems, Diff. Uravn., 1993, vol. 29, no. 4, pp. 585–596.
Kalinin, A.I., An Algorithm for Asymptotically Solving the Terminal Control Problem for Nonlinear Singularly Perturbed Systems, Zh. Vychisl. Mat. Mat. Fiz., 1993, vol. 33, no. 12, pp. 1762–1775.
Kalinin, A.I., Asymptotic Solutions to Perturbed Optimal Control Problems, Izv. Ross. Akad. Nauk, Tekh. Kibern., 1994, no. 3, pp. 104–114.
Kalinin, A.I., An Asymptotic Method of Solving Singularly Perturbed Linear Quadratic Optimal Control Problems, Zh. Vychisl. Mat. Mat. Fiz., 1998, vol. 38, no. 9, pp. 1473–1483.
Kalinin, A.I., Asimptoticheskie metody optimizatsii vozmushchennykh dinamicheskikh sistem (Asymptotic Optimization Methods for Perturbed Dynamic Systems), Minsk: Ekoperspektiva, 2000.
Kalinin, A.I., Asymptotic Minimization of Quadratic Functionals on the Trajectories of Linear Singularly Perturbed Systems, Vestsi NAN Belarusi, Ser. Fiz.-Mat. Navuk, 2001, no. 1, pp. 51–56.
Kalinin, A.I., Optimization of Perturbed Control Systems, Tr. Inst. Mat. Belarus. Nat. Akad. Nauk, Minsk, 2001, vol. 7, pp. 61–70.
Kalinin, A.I. and Kirillova, F.M., Asymptotic Optimization of Linear Dynamic Systems in the Class of Low-Inertia Controls, Avtom. Telemekh., 1994, no. 4, pp. 38–46.
Kalinin, A.I. and Kirillova, F.M., Asymptotic Minimization of Complete Control Pulses, Zh. Vychisl. Mat. Mat. Fiz., 1997, vol. 37, no. 12, pp. 1427–1438.
Kapustyan, V.E., Asymptotic Analysis of Optimal Control for Particle Transport Processes, Avtomatika, 1989, no. 6, pp. 56–59.
Kapustyan, V.E., Asymptotes of Bounded Controls in Optimal Bilinear Elliptical Problems, Dokl. Akad. Nauk. Ukrainy, 1992, no. 9, pp. 35–39.
Kapustyan, V.E., Asymptotic Behavior of Controls in Optimal Singularly Perturbed Parabolic Problems. Global Control Constraints, Dokl. Ross. Akad. Nauk, 1993, vol. 333, no. 4, pp. 428–431.
Kopeikina, T.B., Controllability of Linear Singularly Perturbed Delay Systems, Diff. Uravn., 1989, vol. 25, no. 9, pp. 1508–1518.
Kopeikina, T.B., Stabilization of Linear Singularly Perturbed Delay Systems, Dokl. Belarus. Nat. Akad. Nauk, 1998, vol. 42, no. 3, pp. 22–27.
Kopeikina, T.B., Control of Time-varying Singularly Perturbed Systems, Tr. Inst. Mat. Belarus. Nat. Akad. Nauk, 1999, vol. 3, pp. 71–78.
Kopeikina, T.B. and Tsekhan, O.B., Observability of Linear Singularly Perturbed Systems in the State Space, Prikl. Mat. Mekh., 1993, vol. 57, no. 6, pp. 22–32.
Kopeikina, T.B. and Tsekhan, O.B., A State Space Method for Investigating the Identifiability of Linear Time-varying Singularly Perturbed Systems, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1998, no. 4, pp. 5–14.
Kopeikina, T.B. and Tsekhan, O.B., Observability of Linear Time-varying Singularly Perturbed Systems, Vestsi Akad. Nauk Belarusi, Ser. Fiz.-Mat. Navuk, 1999, no. 3, pp. 22–27.
Korovin, S.K., Mamedov, I.G., and Mamedova, I.P., Uniform Stability Relative to a Small Parameter and Stabilization of Discrete Singularly Perturbed Dynamic Systems, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1989, no. 1, pp. 21–29.
Kostyukova, O.I., An Optimality Criterion for Linear Quadratic Optimal Control of a Descriptor System, Diff. Uravn., 2000, vol. 36, no. 11, pp. 1475–1481.
Kremlev, A.G., Asymptotic Properties of the Trajectories of a Singularly Perturbed System in Optimal Control Problems, Avtom. Telemekh., 1993, no. 9, pp. 61–78.
Kremlev, A.G., Approximation of the Optimal Solution of a Minimax Control Problem for a Singularly Perturbed Quasilinear System, Izv. Akad. Nauk, Tekh. Kibern., 1994, no. 6, pp. 183–193.
Kremlev, A.G., Optimal Control for the Trajectories of a Singularly Perturbed Quasilinear System, Diff. Uravn., 1994, vol. 30, no. 11, pp. 1892–1904.
Kremlev, A.G., Design of Asymptotic Information Sets for Singularly Perturbed Systems, Avtom. Telemekh., 1996, no. 7, pp. 32–42.
Kremlev, A.G., Asymptotic Information Sets in Singularly Perturbed Optimal Control Problems, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1997, no. 1, pp. 79–84.
Kurbitskii, G.M. and Loskutov, P.B., Operative Realization of Optimal Trajectories via Splicing Asymptotic Expansions, in Optimiz. zadachi dinam. poleta (Flight Optimization Problems), Moscow: Mosk. Aviatsion. Inst., 1990, pp. 47–53.
Kurina, G.A., Complete Controllability of a Class of Linear Singularly Perturbed Systems, Diff. Uravn., 1985, vol. 21, no. 8, pp. 1444–1446.
Kurina, G.A., An Asymptotic Solution of a Matrix Singularly Perturbed Riccati Equation, Dokl. Akad. Nauk SSSR, 1988, vol. 301, no. 1, pp. 26–30.
Kurina, G.A., An Asymptotic Solution of a Matrix Singularly Perturbed Riccati Equation under an Infinitely Large Initial Condition, Izv. Ross. Akad. Nauk, Tekh. Kibern., 1992, no. 1, pp. 83–89.
Kurina, G.A., Complete Controllability of Multi-Time-Scale Singularly Perturbed Systems, Mat. Zametki, 1992, vol. 52, no. 4, pp. 56–61.
Kurina, G.A., Singular Perturbation of Control Problems with State Equation not Solvable for the Derivative: A Review, Izv. Ross. Akad. Nauk, Tekh. Kibern., 1992, no. 4, pp. 20–48.
Kurina, G.A., Splitting of Linear Systems not Solvable for the Derivativee, Izv. VUZov. Mat., 1992, no. 4, pp. 26–33.
Kurina, G.A., Splitting of a Two-Point Boundary Problem in Optimal Control, Ukr. Mat. Zh., 1992, vol. 44, no. 5, pp. 704–709.
Kurina, G.A., The Behavior of Reachable Sets of Linear Matrix Singularly Perturbed Systems, Tr. MIRAN, 1995, vol. 211, pp. 316–325.
Kurina, G.A., Higher-Order Approximations in the Small Parameter for Weakly Controllable Systems, Dokl. Ross. Akad. Nauk, 1995, vol. 343, no. 1, pp. 28–32.
Kurina, G.A., A Direct Scheme of Design of Asymptotic Solutions for Weak Control Problems, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1995, no. 6, pp. 162–167.
Kurina, G.A., A Feedback Control for a Linear Quadratic Optimal Control Problem under Legendre Degenerate Condition, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2000, no. 2, pp. 85–89.
Kurina, G.A., An Asymptotic Solution of Optimal Control Problems for Discrete Weakly Controllable Systems, Prikl. Mat. Mekh., 2002, vol. 66, no. 2, pp. 214–227.
Kurina, G.A. and Dolgopolova, E.Yu., Singulyarnye vozmushcheniya v zadachakh upravleniya. Bibliograf. ukazatel’ 1982–2002 (Singular Perturbations in Control Problems: A Bibliographic Index for 1982–2002), Voronezh: VGLTA, 2004.
Kurina, G.A. and Martynenko, G.V., Reducibility of a Nonnegative Hamiltonian Real Periodic Matrix to Block Diagonal Form, Mat. Zametki, 1999, vol. 66, no. 5, pp. 688–695.
Kurina, G.A. and Martynenko, G.V., Reducibility of a Class of Operator Functions to Block Diagonal Form, Mat. Zametki, 2003, vol. 74, no. 5, pp. 789–792.
Kurina, G.A. and Ovezov, Kh.A., Asymptotic Analysis of Matrix Singularly Perturbed Linear Quadratic Optimal Control Problems, Izv. VUZov. Mat., 1996, no. 12, pp. 63–74.
Kurina, G.A., Shchekunskikh, S.S., An Asymptotic Solution for a Linear Quadratic Periodic Problem with Matrix Singular Perturbations in the Quality Criterion, Diff. Uravn., 2005, vol. 45, no. 4, pp. 620–623.
Lomov, S.A., Vvedenie v obshchuyu teoriyu singulyarnykh vozmushchenii (Introduction of General Theory of Singular Perturbations), Moscow: Nauka, 1981.
Mel’nik, T.A., Asymptotic Solution of Discontinuous Singularly Perturbed Boundary-Value Problems, Ukr. Mat. Zh., 1999, vol. 51, no. 6, pp. 861–864.
Miroshnik, I.V., Nikiforov, V.O., and Fradkov, A.V., Nelineinoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (Nonlinear Adaptive Controls for Complex Dynamic Systems), St. Petersburg: Nauka, 2000.
Mikhailova, T.F., Singular Perturbations in the Design of Optimal Controls for Distributed-Parameter Systems, Preprint of Inst. of Cybernetics, Ukrainian Academy of Sciences, 1989, no. 10.
Mikheev, Yu.V., Suboptimal Asymptotic Gradient Control Algorithms for Heat Conductivity Problems, Avtom. Telemekh., 1990, no. 11, pp. 54–62.
Naplatanov, N.D., Zapryanov, I.D., and Mikhailov, L.K., A Hierarchial Suboptimal Control for High-Dimensional Nonlinear Mechanical Systems, Komp. Sist. Upravlen., 1985, vol. 3, pp. 24–33.
Naumenko, K.I., Nablyudenie i upravlenie dvizheniem dinamicheskikh sistem (Observation and Control of the Motion of Dynamic Systems), Kiev: Naukova Dumka, 1984.
Ovseevich, A.I. and Figurina, T.Yu., Asymptotic Behavior of Reachable Domains of Singularly Perturbed Linear Autonomous Control Systems, Prikl. Mat. Mekh., 1998, vol. 62, no. 6, pp. 977–983.
Pasynkov, V.N., A Direct Solution Scheme of Optimal Design for Singularly Perturbed Parabolic Equations, Izv. Akad. Nauk TSSR, Ser. FTKh GN, 1988, no. 1, pp. 8–12.
Pendyukhova, N.V. and Sobolev, V.A., The Symbolic Computation Packet SLOWMAN for Analysis of Singularly Perturbed Systems, in Intellektualizatsiya programmnykh sredstv (Intelligent Software Tools), Novosibirsk: Nauka, 1990, pp. 205–212.
Pliss, P.V., The Structure of Controllability Sets of the Van der Pol Equation with a Small Parameter at the Derivative, Vestn. S.-Peterburg. Univ., 1992, no. 2, pp. 38–41.
Plotnikov, V.A., Metod usredneniya v zadachakh upravleniya (An Averaging Method for Control Problems), Kiev: Libid’, 1992.
Plotnikov, V.A. and Yatsenko, T.P., An Asymptotic Design for the Reachable Domain of a Linear Singularly Perturbed Control System, Izv. VUZov Mat., 1987, no. 7, pp. 73–76.
Ramazanov, M.D., An Asymptotically Optimal Solution for Perturbation Problems, in Asimptot. metody resheniya zadach mat. fiz. (Asymptotic Solution Methods for Problems in Mathematical Physics), Ufa, 1989, pp. 96–108.
Sobolev, V.A., Singular Perturbations in a Linear Quadratic Optimal Control Problem, Avtom. Telemekh., 1991, no. 2, pp. 53–64.
Strygin, V.V. and Sobolev, V.A., Razdelenie dvizhenii metodom integral’nykh mnogoobrazii (Separation of Motion by the Integral Manifold Method), Moscow: Nauka, 1988.
Subbotina, N.N., Asymptotic Properties of Minimax Solutions of Isaacs-Bellman Equations in Differential Games with Fast and Slow Motions, Prikl. Mat. Mekh., 1996, vol. 60, no. 6, pp. 901–908.
Figurina, T.Yu., Asymptotic Behavior of Reachable Domains of Linear Autonomous Control Systems with a Small Parameter at Derivatives, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1998, no. 1, pp. 18–21.
Filatov, O.P., Averaging of Control Differential Equations, Diff. Uravn., 1997, vol. 33, no. 6, pp. 782–785.
Filatov, O.P. and Khapaev, M.M., Usrednenie sistem differentsial’nykh vklyuchenii (Averaging of Differential Inclusion Systems), Moscow: Mosk. Gos. Univ., 1998.
Fradkov, A.L., Adaptivnoe upravlenie v slozhnykh sistemakh: bespoiskovye metody (Adaptive Control for Complex Systems: Searchless Methods), Moscow: Nauka, 1990.
Fridman, L.M., Separation of Motions in Multi-Time-Scaled Discontinuous Control Systems with Delay, Avtom. Telemekh., 1997, no. 7, pp. 240–254.
Chistyakov, V.F., Algebro-differentsial’nye operatory s konechnomernym yadrom (Algebraic Differential Operators with Finite-Dimensional Kernel), Novosibirsk: Nauka, 1996.
Chistyakov, V.F. and Shcheglova, A.A., Controllability of Linear Algebraic Differential Systems, Avtom. Telemekh., 2002, no. 3, pp. 62–65.
Yatsenko, T.P., Linear Quadratic Control Problems: Asymptotic Investigation, Ukr. Mat. Zh., 1988, vol. 40, no. 4, pp. 501–507.
Asamoah, F. and Jamshidi, M., Stabilization of a Class of Singularly Perturbed Bilinear Systems, Int. J. Control, 1987, vol. 46, no. 5, pp. 1589–1594.
Banov, A.M., Golovanov, P.A., Mikheev, Y.V., and Tyomkin, L.S., Perturbation Technique in Thermal Field Control Problems, Proc. 12 IMACS World Congr. Sci. Comput., Paris, 1988, vol. 5, pp. 194–196.
Belokopytov, S.V. and Dmitriev, M.G., Direct Scheme in Optimal Control Problems with Fast and Slow Motions, Syst. Control Lett., 1986, vol. 8, no. 2, pp. 129–135.
Bensoussan, A., Un Résultat de perturbations singuliéres pour systémes distribués instables, C. R. Acad. Sci. Ser. 1, 1983, vol. 296, no. 11. pp. 469–472.
Bensoussan, A. and Blankenship, G.L., Singular Perturbations in Stochastic Control, in Singular Perturbations and Asymptotic Analysis in Control Systems, Lect. Notes in Control Inform. Sci., 1986, pp. 171–263.
Bensoussan, A., Perturbation Methods in Optimal Control Problems, New York: Wiley, 1989.
Binning, H.S. and Goodal, D.P., Constrained Output Feedbacks for Singularly Perturbed Imperfectly Known Nonlinear Systems, J. Franklin Inst., 1999, vol. 336, pp. 449–472.
Chen, C.-C., Global Exponential Stabilization for Nonlinear Singularly Perturbed Systems, IEE Proc. Control Theory Appl., 1998, vol. 145, no. 4, pp. 377–382.
Chenumalla Shailaja and Singh Sahjendra, N., Control of Elastic Spacecraft by Nonlinear Inversion and Singular Perturbation, Proc. 33 IEEE Conf. Decision and Control, 1994, vol. 1, pp. 927–932.
Chuang, C-H., Speyer, J.L., and Breakwell, J.V., An Asymptotic Expansion for an Optimal Relaxation Oscillator, SIAM J. Control Optimiz., 1988, vol. 26, no. 3, pp. 678–696.
Dmitriev, A.M., Construction of Approximately Invariant Strategies in Singularly Perturbed Control Systems with Uncertainty, Proc. 2 Int. Conf. Control of Oscillations and Chaos, St. Petersburg, 2000, vol. 1, pp. 137–139.
Dmitriev, M.G., Dontchev, A.L., and Veliov, V.M., A Regularized Conditional Gradient Method in Singularly Perturbed Optimal Control Systems, Serdika B"lg. Mat. Spisanie, 1985, vol. 11, no. 2, pp. 180–185.
Dmitriev, M.G. and Kang Ni Ming, Contrast Structures in Simple Variational Vector Problems and Its Asymptotes, Proc. IFAC Workshop “Singular Solutions and Perturbations in Control Systems,” 1997, Pereslavl-Zalessky, Russia, Oxford: Elsevier Science, 1998, pp. 13–18.
Dontchev, A.L. and Veliov, V.M., A Singularly Perturbed Optimal Control Problem with Fixed Final State and Constrained Control, Contr. Cyber., 1982, vol. 11, no. 1–2, pp. 19–28.
Dontchev, A.L. and Veliov, V.M., Singular Perturbations in Mayer’s Problem for Linear Systems, SIAM J. Control Optimiz., 1983, vol. 21, no. 4, pp. 566–581.
Dragan, V., Cheap Control with Several Scales, Rev. Roumaine Math. Pures Appl., 1988, vol. 33, no. 8, pp. 663–677.
Dragan, V. and Halanay, A., High-Gain Feedback Stabilization of Linear Systems, Int. J. Control, 1987, vol. 45, no. 2, pp. 549–577.
Dragan, V. and Halanay, A., Uniform Controllability for Systems with Two Time-Scales, Rev. Roumaine Math. Pures Appl., 1992, vol. 37, no. 8, pp. 673–681.
Dragan, V. and Stoica, A., Some Singular Perturbation Techniques in Robust Control, Rev. Roumaine Sci. Techn. Ser. Electrotechn. Et énerg., 2000, vol. 45, no. 3, pp. 337–348.
11 IFAC World Congress. Preprints, vol. 6, Tallinn, Estonia, USSR, 1990.
Fridman, E., Exact Decomposition of Linear Singularly Perturbed H ∞-Optimal Control Problems, Kybernetika, 1995, vol. 31, no. 6, pp. 591–599.
Fridman, E., H ∞-Control of Nonlinear Singularly Perturbed Systems and Invariant Manifolds, in New Trends in Dynamic Games and Applications, Olsder, G., Ed., Boston: Birkhauser, 1995, pp. 25–45.
Fridman, E., Exact Slow-Fast Decomposition of Nonlinear Singularly Perturbed Optimal Control Problems, Syst. Control Lett., 2000, vol. 40, pp. 121–131.
Fridman, E., State-Feedback H ∞ Control of Nonlinear Singularly Perturbed Systems, Int. J. Robust Nonlinear Control, 2001, vol. 11, no. 12, pp. 1115–1125.
Fridman, E., A Descriptor System Approach to Nonlinear Singularly Perturbed Optimal Control Problems, Automatica, 2001, vol. 37, no. 4, pp. 543–549.
Fridman, E. and Shaked, U., Robust H ∞ Minimum Entropy Static Output-Feedback Control of Singularly Perturbed Systems, Automatica, 2000, vol. 36, pp. 1181–1188.
Gaitsgory, V., Suboptimization of Singularly Perturbed Control Systems, SIAM J. Control Optimiz., 1992, vol. 30, no. 5, pp. 1228–1249.
Gaitsgory, V., Limit Hamilton-Jacobi-Isaacs Equations for Singularly Perturbed Zero-Sum Differential Games, Int. J. Math. Anal. Appl., 1996, vol. 202, pp. 862–899.
Gaitsgory, V., Leizarowitz, A., Limit Occupational Measures Set for a Control System and Averaging of Singularly Perturbed Control Systems, J. Math. Anal. Appl., 1999, vol. 233, pp. 461–475.
Gaitsgory, V. and Nguyen Minh-Tuan, Averaging of Three Time Scale Singularly Perturbed Control Systems, Syst. Control Lett., 2001, vol. 42, no. 5, pp. 395–403.
Gajic, Z. and Lim, M., Optimal Control of Singularly Perturbed Linear Systems and Applications. High-Accuracy Techniques, New York: Marcel Dekker, 2000.
Gajic, Z., Petkovski, D., and Harkara, N., The Recursive Algorithm for The Optimal Static Output Feedback Control Problem of Linear Singularly Perturbed Systems, IEEE Trans. Automat. Control, 1989, vol. 34, no. 4, pp. 465–468.
Gajic, Z., Petkovski, D., and Shen, X., Singularly Perturbed and Weakly Coupled Linear Control Systems: A Recursive Approach, Berlin: Springer, 1990.
Garofalo, F. and Leitman, G., Nonlinear Composite Control of a Nominally Linear Singularly Perturbed Uncertain System, Proc. 12 IMACS World Congr. Sci. Comput., Paris, 1988, vol. 2, pp. 83–86.
Glizer, V.Y., Asymptotic Solution of Singularly Perturbed Infinite-Dimensional Riccati Equations, J. Math. Anal. Appl., 1997, vol. 214, pp. 63–88.
Glizer, V.Y., Asymptotic Solution of a Singularly Perturbed Set of Functional-Differential Equations of Riccati Type Encountered in the Optimal Control Theory, Nonlinear Diff. Eq. Appl., 1998, vol. 5, no. 4, pp. 491–515.
Glizer, V.Y., Stabilizability and Detectability of Singularly Perturbed Linear Time-Invariant Systems with Delays in State and Control, J. Dyn. Control Syst., 1999, vol. 5, no. 2, pp. 153–172.
Glizer, V.Y., Asymptotic Solution of a Zero-Sum Linear-Quadratic Differential Game with Cheap Control for Minimizer, Nonlinear Diff. Eq. Appl., 2000, vol. 7, no. 2, pp. 231–258.
Glizer, V.Y., Euclidean Space Controllability of Singularly Perturbed Linear Systems with State Delay, Syst. Control Lett., 2001, vol. 43, no. 3, pp. 181–191.
Glizer, V.Y., Observability of Singularly Perturbed Linear Time-Dependent Differential Systems with Small Delay, J. Dyn. Control Syst., 2004, vol. 10, no. 3, pp. 329–363.
Glizer, V.Y. and Fridman, E., H ∞Control of Linear Singularly Perturbed Systems with Small State Delay, J. Math. Anal. Appl., 2000, vol. 250, pp. 49–85.
Henry, J. and Pierret, C., Identification of Systems with Fast and Slow Dynamics. Application to Cardiac Action Potential, Proc. 25 IEEE Conf. Decision and Control, Athens, 1986, vol. 1, pp. 277–281.
Ioannou, P.A. and Kokotovic, P.V., Adaptive Systems with Reduced Models, Lecture Notes in Control Inform. Sci., vol. 47, Berlin: Springer-Verlag, 1983.
Ioannou, P. and Kokotovic, P., Decentralized Adaptive Control in the Presence of Multiparameter Singular Perturbations and Bounded Disturbances, Proc. Am. Control Conf., San Francisco, 1983, vol. 2, pp. 553–558.
Kalinin, A.I. and Polevikov, S.V., Asymptotic Solution of the Minimum Force Problem for Linear Singularly Perturbed Systems, Automatica, 1998, vol. 34, no. 5, pp. 625–630.
Kamenski, M., Nistri, P., and Quincampoix, M., Sliding Mode Control of Uncertain Systems: A Singular Perturbation Approach, IMA J. Math. Control Inform., 2002, vol. 19, pp. 377–398.
Kapustyan, V.E., Asymptotic Analysis of Optimal Control Problems for Singularly Perturbed Periodical Parabolical Systems, Proc. Int. Workshop “Singular Solutions and Perturbations Control Systems,” Pereslavl-Zalessky, 1995, pp. 45–47.
Khalil, H. and Chen, F., H ∞ Control of Two-Time-Scale Systems, Syst. Control Lett., 1992, vol. 19, pp. 35–42.
Kimura, M., On the Matrix Riccati Equation for a Singularly Perturbed Linear Discrete Control System, Int. J. Control, 1983, vol. 38, no. 5, pp. 959–975.
Kokotovic, P.V., Application of Singular Perturbation Techniques to Control Problems, SIAM Review, 1984, vol. 26, no. 4, pp. 501–550.
Kokotovic, P.V., Khalil, H.K., and O’Reilly, J., Singular Perturbation Methods in Control: Analysis and Design, London: Academic, 1986.
Kokotovic, P.V., Khalil, H.K., and O’Reilly, J., Singular Perturbation Methods in Control: Analysis and Design, Philadelphia: SIAM, 1999.
Kokotovic, P.V., O’Malley, R.E., Jr., and Sannuti, P., Singular Perturbations and Order Reduction in Control Theory: An Overview, Automatica, 1976, vol. 12, no. 2, pp. 123–132.
Komornik, V., Perturbations Singuliéres de Systémes Distriués Instables, C. R. Acad. Sci., 1983, sér. 1, vol. 296, no. 19, pp. 797–799.
Kopeikina, T.B., The Qualitative Theory of Control Processes, Notes Mat. Univ. Andes, 2001, no. 215, pp. 1–73.
Kremlev, A.G., Asymptotic Approximation of Sets of Possible States of Singularly Perturbed Quasilinear Systems, Abstracts. Int. Conf. “Dynamical Systems: Stability, Control, and Optimization,” Minsk, 1998, vol. 2, pp. 162–165.
Kurina, G.A., Feedback Control for Time-Varying Descriptor Systems, Syst. Sci., 2001, vol. 26, no. 3, pp. 47–59.
Kurina, G.A., Feedback Control for Discrete Descriptor Systems, Syst. Sci., 2002, vol. 28, no. 2, pp. 29–40.
Kurina G.A., Linear-Quadratic Discrete Optimal Control Problems for Descriptor Systems in Hilbert Space, J. Dyn. Control Syst., 2004, vol. 10, no. 3, pp. 365–375.
Kurina, G.A. and März, R., On Linear-Quadratic Optimal Control Problems for Time-Varying Descriptor Systems, SIAM J. Control Optimiz., 2004, vol. 42, no. 6, pp. 2062–2077.
Kurina, G.A. and Shabanova, S.S., Asymptotic Solution of Periodic Control Problem Perturbed by Matrix, IFAC Workshop on Singular Solutions and Perturbations in Control Systems, 1997, Pereslavl-Zalessky, Russia, Elsevier Science Oxford, 1998, pp. 37–42.
Lee, J.T. and Bien, Z.N., A Quadratic Regulator with Cheap Control for a Class of Nonlinear Systems, J. Optimiz. Theory Appl., 1987, vol. 55, no. 2, pp. 289–302.
Leitmann, G., Controlling Singularly Perturbed Uncertain Dynamical Systems, in Model and Contr. Syst. Eng., Quantum Mech., Econ. and Biosci., Proc. Bellman Contin. Workshop, Sophia Antipolis, 1988, Berlin, 1989, pp. 3–14.
Lewis, F.L., A Survey of Linear Singular Systems, Circuits, Syst. Signal Proc., 1986, vol. 5, no. 1, pp. 3–36.
Lions, J.L., Exact Controllability and Singular Perturbations. Wave Motion: Theory, Modelling and Comput., Proc. Conf. Hon. 60 birthday Peter D.Lax., New York, 1987, pp. 217–247.
Lions, J.L., Controlabilité Exacte et Perturbations Singuliéres (II): La Methode de Dualité, Appl. Multiple Scaling Mech., Proc. Int. Conf., Ec. Norm. Super., Paris, 1987, pp. 223–227.
Litkouhi, B. and Khalil, H., Infinite-Time Regulators for Singularly Perturbed Difference Equations, Int. J. Control, 1984, vol. 39, pp. 587–598.
Mahmoud Magdi, S., Stabilization of Discrete Systems with Multiple-Time Scales, IEEE Trans. Automat. Control, 1986, vol. 31, no. 2, pp. 159–162.
O’Malley, R.E., Jr., Singular Perturbations and Optimal Control, Lect. Notes Math., 1978, vol. 680, pp. 171–218.
Mc Clamroch, N.H. and Krishnan, H., Non-Standard Singularly Perturbed Control Systems and Differential-Algebraic Equations, Int. J. Control, 1992, vol. 55, no. 5, pp. 1239–1253.
Marino, R. and Kokotovic, P., A Geometric Approach to Composite Control of Two-Time-Scale Systems, Proc. 25 IEEE Conf. Decision and Control, Athens, 1986, vol. 2, pp. 1397–1399.
Mehrmann, V.L., The Autonomous Linear Quadratic Control Problem, Lect. Notes Control Inform. Sci., 1991, vol. 163.
Mizukami, K. and Xu, H., Near-Optimal Incentive Stackelberg Strategies for Singularly Perturbed Systems, Proc. 11 Trienn. IFAC World Congress, Tallinn, 1990, vol. 3, pp. 427–432.
Moiseev, N.N. and Chernousko, F.L., Asymptotic Methods in the Theory of Optimal Control, IEEE Trans. Automat. Control, 1981, vol. 26, no. 5, pp. 993–1000.
Naidu, D.S., Singular Perturbation Methodology in Control Systems, IEE Control Eng. Seriers, 1988, no. 34.
Naidu, D.S., Singular Perturbations and Time Scales in Control Theory and Applications: An Overview, Dynamic Continuous, Discrete and Impulsive Syst., Ser. B: Appl. and Algorithms, 2002, vol. 9, pp. 233–278.
Naidu, D.S. and Calise, A.J., Singular Perturbations and Time Scales in Guidance and Control of Aerospace Systems: A Survey, AIAA J. Guidance, Control Dynam., 2001, vol. 24, pp. 1057–1078.
Naidu, D.S., Charalambous, C.D., Moore, K.L., and Abdelrahman, M.A., H ∞-Optimal Control of Singularly Perturbed Discrete-Time Systems, and Risk-Sensitive Control, Proc. 33 IEEE Conf. Decision and Control, Lake Buena Vista, Fla., 1994, vol. 2, pp. 1706–1711.
Naidu, D.S. and Rao, A.K., Singular Perturbation Analysis of Discrete Control Systems, Lect. Notes Math., 1985, vol. 1154.
Pan, Z. and Basar, T., H ∞-Optimal Control for Singularly Perturbed Systems. I. Perfect State Measurements, Automatica, 1993, vol. 29, pp. 401–424.
Pan, Z. and Basar, T., H ∞-Optimal Control for Singularly Perturbed Systems. II. Imperfect State Measurements, IEEE Trans. Automat. Control, 1994, vol. 39, no. 2, pp. 280–299.
Pan, Z. and Basar, T., Time-Scale Separation and Robust Controller Design for Uncertain Nonlinear Singularly Perturbed Systems under Perfect State Measurements, Int. J. Robust Nonlinear Control, 1996, vol. 6, pp. 585–608.
Pan, Z. and Basar, T., Model Simplification and Optimal Control of Stochastic Singularly Perturbed Systems under Exponentiated Quadratic Cost, SIAM J. Control Optimiz., 1996, vol. 34, no. 5, pp. 1734–1766.
Ryan, E.P. and Yacob, Z.B., Singularly Perturbed Uncertain Systems and Dynamic Output Feedback Control, Model and Control System Engineering, Quantum Mechanics, Economics and Biosciences, Proc. Bellman Contin. Workshop, Sophia Antipolis, 1988, pp. 37–50.
Saberi, A. and Khalil, H., Stabilization and Regulation of Nonlinear Singularly Perturbed Systems-Composite Control, IEEE Trans. Automat. Control, 1985, vol. 30, no. 8, pp. 739–747.
Saberi, A. and Sannuti, P., Time-Scale Decomposition of a Class of Linear and Nonlinear Cheap Control Problems, Proc. Am. Control Conf., Boston, 1985, vol. 3, pp. 1414–1421.
Saberi, A. and Sannuti, P., Cheap and Singular Controls for Linear Quadratic Regulators, IEEE Trans. Automat. Control, 1985, vol. 32, no. 3, pp. 208–219.
Saksena, V.R. and Cruz, J.B., Jr., Robust Nash Strategies for a Class of Nonlinear Singularly Perturbed Problems, Int. J. Control, 1984, vol. 39, no. 2, pp. 293–310.
Saksena, V.R., O’Reilly, J., and Kokotovic, P.V., Singular Perturbations and Time-Scale Methods in Control Theory: A Survey 1976–1983, Automatica, 1984, vol. 20, no. 3, pp. 273–293.
Sannuti, P., Direct Singular Perturbation Analysis of High Gain and Cheap Control Problems, Automatica, 1983, vol. 19, no. 1, pp. 41–51.
Sannuti, P. and Wason, H., Multiple Time-Scale Decomposition in Cheap Control Problems—Singular Control, IEEE Trans. Automat. Control, 1985, vol. 30, no. 8, pp. 633–644.
Singular Perturbations and Asymptotic Analysis in Control Systems, Lect. Notes Control Inform. Sci., Kokotovic, P., Bensoussan, A., and Blankenship, G., Eds., Berlin: Springer-Verlag, 1987.
Singular Perturbations in Systems and Control, International Centre for Mechanical Sciences, Courses and Lectures, no. 280, Ardema, M.D., Ed., New York: Springer-Verlag, 1983.
Singular Perturbations in Systems and Control, Kokotovic, P.V. and Khalil, H.K., Eds., New York: IEEE Press, 1986.
Singular Solutions and Perturbations in Control Systems, Proc. Int. Workshop “Singular Solutions and Perturbations in Control Systems,” Pereslavl-Zalessky, 1993.
Singular Solutions and Perturbations in Control Systems, Proc. Int. Workshop “Singular Solutions and Perturbations in Control Systems,” Pereslavl-Zalessky, 1995.
Singular Solutions and Perturbations in Control Systems, Proc. Int. Workshop “Singular Solutions and Perturbations in Control Systems,” Pereslavl-Zalessky, 1997.
Sobolev, V.A., Integral Manifolds and Decomposition of Singularly Perturbed Systems, Syst. Control Lett., 1984, vol. 5, pp. 169–179.
Su, W.C., Gajic, Z., and Shen, X.M., Exact Slow-Fast Decomposition of the Algebraic Riccati Equation of Singularly Perturbed Systems, IEEE Trans. Automat. Control, 1992, vol. 37, no. 9, pp. 1456–1459.
Syrcos, G.P. and Sannuti, P., Singular Perturbation Modeling and Design Techniques Applied to Jet Engine Control, Optim. Control Appl. Methods, 1986, vol. 7, no. 1, pp. 1–17.
Tan, W., Leung, T., and Tu, Q., H ∞Control for Singularly Perturbed Systems, Automatica, 1998, vol. 34, no. 2, pp. 255–260.
Tran Minh, T. and Sawan Mahmoud, E., Nash Strategies for Discrete-Time Systems with Slow and Fast Modes, Int. J. Syst. Sci., 1983, vol. 14, no. 12, pp. 1355–1371.
Tuan, H.D. and Hosoe, S., On Linear Robust H ∞Controllers for a Class of Nonlinear Singular Perturbed Systems, Automatica, 1999, vol. 35, no. 4, pp. 735–739.
Van Harten, A., Singularly Perturbed Systems of Difusion Type and Feedback Control, Automatica, 1984, vol. 20, no. 1, pp. 79–91.
Vian John, L. and Sawan, M.E., H ∞Control for a Singularly Perturbed Aircraft Model, Optim. Control Appl. Meth., 1994, vol. 15, no. 4, pp. 277–289.
Voropaeva, N.V., Computer Algebra Methods in Aircraft Control and Dynamics, Proc. Int. Congr. Comput. Syst. Appl. Math., St. Petersburg, 1993, p. 116.
Xu, H. and Mizukami, K., Nonstandard Extension of H ∞-Optimal Control for Singularly Perturbed Systems, Proc. 7 Int. Symp. Dynamic Games Appl., Kanagawa, 1996, pp. 931–948.
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Original Russian Text © M.G. Dmitriev, G.A. Kurina, 2006, published in Avtomatika i Telemekhanika, 2006, No. 1, pp. 3–51.
The work of the first author was supported by the Russian Foundation for Basic Research, project nos. 04-01-00536a and 05-06-80237a and that of the second author by a grant of the Russian President to Leading Russian Scientific Schools, project no. Nsh-1 643.2003.1.
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Dmitriev, M.G., Kurina, G.A. Singular perturbations in control problems. Autom Remote Control 67, 1–43 (2006). https://doi.org/10.1134/S0005117906010012
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DOI: https://doi.org/10.1134/S0005117906010012